Opgave 10 Oefening 2

*Unverified author*

R Software Module: /rwasp_exponentialsmoothing.wasp (opens new window with default values)

Title produced by software: Exponential Smoothing

Date of computation: Thu, 19 May 2011 15:11:19 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2011/May/19/t130581763593dshivmp7se06a.htm/, Retrieved Thu, 19 May 2011 17:07:16 +0200

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

KDGP2W102

Dataseries X:

» Textbox « » Textfile « » CSV «

8 8 8,2 8,5 8,7 8,7 8 8 8,3 8,5 8,7 8,6 8,3 7,9 7,9 8,1 8,3 8,1 7,4 7,3 7,7 8 8 7,7 6,9 6,6 6,9 7,5 7,9 7,7 6,5 6,1 6,4 6,8 7,1 7,3 7,2 7 7 7 7,3 7,5 7,2 7,7 8 7,9 8 8 7,9 7,9 8 8,1 8,1 8,2 8 8,3 8,5 8,6 8,7 8,7 8,5 8,4 8,5 8,7 8,7 8,6 7,9 8,1 8,2 8,5 8,6 8,5

Output produced by software:

Summary of computational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 2 seconds R Server 'RServer@AstonUniversity' @ vre.aston.ac.uk Estimated Parameters of Exponential Smoothing Parameter Value alpha 1 beta 0.947401841274698 gamma FALSE Interpolation Forecasts of Exponential Smoothing t Observed Fitted Residuals 3 8.2 8 0.199999999999999 4 8.5 8.38948036825494 0.110519631745062 5 8.7 8.79418687086721 -0.0941868708672136 6 8.7 8.90495405598371 -0.204954055983713 7 8 8.71078020596802 -0.710780205968025 8 8 7.33738573009231 0.66261426990769 9 8.3 7.96514770945775 0.334852290542255 10 8.5 8.58238738607253 -0.0823873860725293 11 8.7 8.7043334248096 -0.00433342480960519 12 8.6 8.90022793016596 -0.300227930165958 13 8.3 8.51579143632464 -0.215791436324636 14 7.9 8.01135023221937 -0.111350232219365 15 7.9 7.50585681718837 0.394143182811627 16 8.1 7.87926879430998 0.220731205690021 17 8.3 8.28838994500749 0.0116100549925129 18 8.1 8.4993893324847 -0.399389332484697 19 7.4 7.92100714350322 -0.521007143503221 20 7.3 6.727404016431 0.572595983569 21 7.7 7.16988250557077 0.530117494429233 22 8 8.07211679588495 -0.072116795884952 23 8 8.30379321067672 -0.303793210676716 24 7.7 8.01597896351484 -0.315978963514843 25 6.9 7.41661991167681 -0.51661991167681 26 6.6 6.12717325611503 0.472826743884971 27 6.9 6.27513018387557 0.624869816124431 28 7.5 7.16713299822884 0.332867001771162 29 7.9 8.08249180860643 -0.182491808606425 30 7.7 8.30959873311515 -0.609598733115148 31 6.5 7.53206377092313 -1.03206377092313 32 6.1 5.35428465403765 0.745715345962352 33 6.4 5.66077674586918 0.739223254130822 34 6.8 6.6611182179458 0.138881782054206 35 7.1 7.19269507398346 -0.0926950739834602 36 7.3 7.40487559021444 -0.104875590214435 37 7.2 7.50551626294051 -0.305516262940508 38 7 7.11606959289131 -0.116069592891306 39 7 6.80610504687008 0.193894953129922 40 7 6.98980148247924 0.0101985175207622 41 7.3 6.99946357675668 0.30053642324332 42 7.5 7.58419233750751 -0.0841923375075133 43 7.2 7.70442836193167 -0.504428361931675 44 7.7 6.92653200304643 0.773467996953574 45 8 8.1593170075273 -0.159317007527296 46 7.9 8.30837978124956 -0.408379781249559 47 8 7.82148002455437 0.178519975445631 48 8 8.09061017799587 -0.0906101779958739 49 7.9 8.00476592852436 -0.104765928524355 50 7.9 7.80551049493753 0.0944895050624721 51 8 7.89503002601485 0.104969973985151 52 8.1 8.09447877264694 0.00552122735306249 53 8.1 8.19970959360732 -0.099709593607324 54 8.2 8.105244541031 0.094755458969006 55 8 8.29501603732906 -0.295016037329058 56 8.3 7.81551730035794 0.484482699642057 57 8.5 8.57451710206457 -0.0745171020645667 58 8.6 8.70391946236214 -0.103919462362141 59 8.7 8.70546597237597 -0.00546597237597268 60 8.7 8.80028750008262 -0.100287500082619 61 8.5 8.70527493784751 -0.205274937847509 62 8.4 8.31079708376323 0.0892029162367702 63 8.5 8.29530809085302 0.20469190914698 64 8.7 8.5892335824729 0.110766417527097 65 8.7 8.89417389038947 -0.194173890389475 66 8.6 8.71021318910701 -0.110213189107014 67 7.9 8.50579701081427 -0.605797010814273 68 8.1 7.23186380733012 0.868136192669876 69 8.2 8.25433763474277 -0.0543376347427706 70 8.5 8.30285805953696 0.197141940463043 71 8.6 8.78963069692411 -0.189630696924112 72 8.5 8.709974225496 -0.209974225496003 Extrapolation Forecasts of Exponential Smoothing t Forecast 95% Lower Bound 95% Upper Bound 73 8.41104425764086 7.68450259472618 9.13758592055554 74 8.32208851528172 6.73158046301297 9.91259656755047 75 8.23313277292258 5.59625069421242 10.8700148516327 76 8.14417703056345 4.30415823452818 11.9841958265987 77 8.0552212882043 2.87303106563858 13.23741151077 78 7.96626554584517 1.31579274973827 14.6167383419521 79 7.87730980348603 -0.35764077004449 16.1122603770166 80 7.7883540611269 -2.13936224127287 17.7160703635267 81 7.69939831876775 -4.02287946231933 19.4216760998548 82 7.61044257640861 -6.00273982171097 21.2236249745282 83 7.52148683404948 -8.07428037155245 23.1172540396514 84 7.43253109169034 -10.2334544009284 25.0985165843091

Charts produced by software:

http://www.freestatistics.org/blog/date/2011/May/19/t130581763593dshivmp7se06a/1e19g1305817875.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t130581763593dshivmp7se06a/1e19g1305817875.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t130581763593dshivmp7se06a/29vo51305817875.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t130581763593dshivmp7se06a/29vo51305817875.ps (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t130581763593dshivmp7se06a/3rs221305817875.png (open in new window) http://www.freestatistics.org/blog/date/2011/May/19/t130581763593dshivmp7se06a/3rs221305817875.ps (open in new window)

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ;

Parameters (R input):

par1 = 12 ; par2 = Double ; par3 = additive ;

R code (references can be found in the software module):

par1 <- as.numeric(par1) if (par2 == 'Single') K <- 1 if (par2 == 'Double') K <- 2 if (par2 == 'Triple') K <- par1 nx <- length(x) nxmK <- nx - K x <- ts(x, frequency = par1) if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F) if (par2 == 'Double') fit <- HoltWinters(x, gamma=F) if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3) fit myresid <- x - fit$fitted[,'xhat'] bitmap(file='test1.png') op <- par(mfrow=c(2,1)) plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing') plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors') par(op) dev.off() bitmap(file='test2.png') p <- predict(fit, par1, prediction.interval=TRUE) np <- length(p[,1]) plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing') dev.off() bitmap(file='test3.png') op <- par(mfrow = c(2,2)) acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF') spectrum(myresid,main='Residals Periodogram') cpgram(myresid,main='Residal Cumulative Periodogram') qqnorm(myresid,main='Residual Normal QQ Plot') qqline(myresid) par(op) dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'Value',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'alpha',header=TRUE) a<-table.element(a,fit$alpha) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'beta',header=TRUE) a<-table.element(a,fit$beta) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'gamma',header=TRUE) a<-table.element(a,fit$gamma) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Observed',header=TRUE) a<-table.element(a,'Fitted',header=TRUE) a<-table.element(a,'Residuals',header=TRUE) a<-table.row.end(a) for (i in 1:nxmK) { a<-table.row.start(a) a<-table.element(a,i+K,header=TRUE) a<-table.element(a,x[i+K]) a<-table.element(a,fit$fitted[i,'xhat']) a<-table.element(a,myresid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'t',header=TRUE) a<-table.element(a,'Forecast',header=TRUE) a<-table.element(a,'95% Lower Bound',header=TRUE) a<-table.element(a,'95% Upper Bound',header=TRUE) a<-table.row.end(a) for (i in 1:np) { a<-table.row.start(a) a<-table.element(a,nx+i,header=TRUE) a<-table.element(a,p[i,'fit']) a<-table.element(a,p[i,'lwr']) a<-table.element(a,p[i,'upr']) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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